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Week 02 · Rates and Speed

Friday

Rates all around
// A ratio with two different units
⏱ about 20 min

Friday: Rates All Around

Rocket sits at the Numbers Desk with two fingers on his wrist. "Shh. I am counting."

"Counting what?" Raven asks. "Heartbeats," Rocket says. "Eighteen in 15 seconds. That is a rate."

Raven writes it down. "Heartbeats per 15 seconds. Can you make it per minute?"

"Four fifteens in a minute," Rocket says. "So 18 times 4. Seventy-two beats per minute."

Nova circles the kitchen slowly. "Rates are everywhere here. What do you notice about the dripping tap?"

Raven listens. "One drop every 2 seconds. That is a rate too, and a very annoying one."

Rates in everyday life

A rate is anywhere two different units go together: heartbeats per minute, pages per minute, drops per second.

A unit rate makes any two rates easy to compare. Seventy-two beats per minute can be compared with any other count.

Changing units is ratio reasoning too. Four groups of 15 seconds make 1 minute, so multiply a 15-second count by 4.

  • Heartbeats per minute: count for 15 seconds, then multiply by 4.
  • Pages per minute: pages read divided by minutes spent.
  • Growth per week: centimeters gained divided by weeks.
  • Speed: meters divided by seconds.
REVIEW: UNIT RATES
  • Read the question.
  • Tap your answer.
A timer counts 72 heartbeats in 60 seconds. How many heartbeats per second?
35 pages in 7 minutes. How many pages per minute?
15 centimeters in 5 weeks. How many centimeters per week?
63 meters in 9 seconds. How many meters per second?
REVIEW: PREDICT AND CHANGE UNITS
  • Read the question.
  • Tap your answer.
Rocket counts 18 heartbeats in 15 seconds. How many heartbeats per minute?
The tap drips 1 drop every 2 seconds. How many drops in 60 seconds?
5 minutes is how many seconds?
300 centimeters is how many meters?
Number sentenceTrue or false?
18 × 4 = 72?
56 ÷ 8 = 7?
36 ÷ 9 = 5?
250 ÷ 100 = 2.5?
2 × 60 = 100?
WHY THIS EXERCISEThe week's rate problems all come down to a careful divide or multiply.
WHICH IS FASTER?
  • Read the question.
  • Tap your answer.
A walker goes 24 meters in 12 seconds. A jogger goes 35 meters in 7 seconds. Who is faster?
Reader A finishes 24 pages in 6 minutes. Reader B finishes 25 pages in 5 minutes. Who reads faster?
Seedling 1 grew 12 centimeters in 4 weeks. Seedling 2 grew 10 centimeters in 5 weeks. Which grew faster?
Which rate is the same speed as 5 meters per second?

Look ahead: percents

Next week the crew counts Field Day sign-ups. A percent is a special rate: a number per 100.

If 10 of 40 kids choose the relay, that is 25 per 100, or 25 percent. You already know how to scale it.

Draw one everyday rate from today as a double number line.

A full week of rates. Tomorrow is Data Day: the family counts heartbeats and steps.

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